I wanted to install dependencies for dropbox, and I found apt trying to
remove some quite important packages... Note that in the remove section there
is compiz or vim... How to proceed, safely, with the apt? I use Ubuntu 12.04 LTS

Do you know if you recently removed any major metapackages such as ubuntu-desktop? (You could have manually done this...or it could have happened automatically as a result of removing a dependency of the metapackage.)

In particular, is ubuntu-desktop installed? If not, installing it may mark the needed packages as being required by a manually installed package, making them no longer subject to autoremoval.

@JakubM. Sorry, of course it is, it's listed as one of the packages to be removed by apt-get autoremove. If you were to set it to manually installed (and do the same with ubuntu-minimal), that might protect many of the important packages from being subject to autoremoval. (You can set a package to manually installed the same way you'd manually install it: sudo apt-get install ubuntu-desktop ubuntu-minimal.) I don't know if this will fix your whole problem, or even if this operation will succeed (depending on what's broken on your system), but it shouldn't hurt.
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Eliah KaganJun 5 '12 at 8:17